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$P$ and $Q$ are the points on the sides DE and DF of a triangle DEF such that $D P = 5 cm, D E = 15 cm$ $D Q = 6 cm$ and $D F = 18 cm .$

Is $P Q ‖ E F ?$

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Yes

Cannot determined

Insufficient Data

answer is A.

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Detailed Solution

Given that,

P

and

Q

are the points on the sides DE and DF of a triangle DEF.

D P = 5 cm, D E = 15 cm D Q = 6 cm

and

D F = 18 cm

We have to find whether

P Q ‖ E F

Now use the proportional theorem
If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.
It means,

D P P E = D Q Q F

Now,

D P P E = D P D E − D P ⇒ D P P E = 5 15 − 5 ⇒ D P P E = 510 ⇒ D P P E = 12

Similarly,

⇒ D Q Q F = D Q D F − D Q ⇒ D Q Q F = 6 18 − 6 ⇒ D Q Q F = 612 ⇒ D Q Q F = 12

Therefore

D P P E = D Q Q F

Hence PQ is parallel to EF.

P

and

Q

are the points on the sides DE and DF of a triangle DEF such that

D P = 5 cm, D E = 15 cm, D Q = 6 cm

and DF=

18 cm

, then PQ is parallel to EF.
So, the correct option is 1.

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